The smart-BLAGE algorithm for singularly perturbed 2D elliptic partial differential equations

We discuss, a new smart block alternating group explicit (smart-BLAGE) algorithm for solving the symmetric block linear systems derived from nine-point fourth-order method based on arithmetic average discretizations to solve the singularly perturbed two-dimensional elliptic equations. The smart-BLAGE algorithm is predicted to save time as the idea involved is to eliminate evaluating two similar terms appearing in the algorithm. The error analysis of the smart-BLAGE algorithm is discussed briefly. Numerical tests are performed to demonstrate the usefulness of the proposed smart-BLAGE method and compared with the corresponding block successive over relaxation (BSOR) method by considering two test problems.